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Consider the Lorenz curve of a country , given by f(x) = x ^ (5/2) for...
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- 4 marks) In economics, a population's Lorenz curve L(2) gives the percentage (as a decimal) of the country's distribution of wealth among the lowest earning percentage 2 (as a decimal between 0 and 1; e.g., 35% means x = 0.35) of the population. As an example, if L(0.4) = 0.1, then this means that the lowest earning 40% of households have only 10% of the entire economy's wealth. The line y =...
For a given population (for example, residents of the United States), the Lorens Pnction measure how wealth is distributed. IfO Sps 1, then L(p)-the percent of total wealth owned by the poorst p percent of the population In other words, if L(2)-. 1, this says that the porest 20% of people own 10% of the wwalth. 1. In terms of income equity, what does it mean if L(p) is cdoswe to p for some value of p? What does it...
2. The following table gives points on the Lorenz curve for the U.S. in 1970. 0 .6 8 .2 .4 L(x) 0 .323 .568 1 041 .149 a) Based on the table, the poorest 20% of the population in 1970 earned what percent of the total income? b) The richest 20% of the population earned what percent of total income in the US, in 1970? Use a calculator or computer to find a quadratic curve best fit with form L(x)...
3. The Gini Index Problem How is possible to measure the distribution of income among the inhabitants of a given country One such measure is the Gini index, named after the Italian economist Corrado Gini, who first devised it in 1912. We first rank all households in a country by income and then we compute the percentage of households whose income is at most a given percentage of the country's total income. We define a Lorenz Curve y L(x) on...
11. (10pts) Consider the curve given by the function f(x) = x2 – 3x + 2 a) Approximate the area of the curve over the interval [0,10) using Reimann Sums. Use midpoints with n = 5 subintervals. b) Find the exact area of the curve over the interval [0,10] using integration.
Question 6 14 pts Consider the curve C defined by the parametric equations: x f(t) y= g(t) = sint -t costt (d) Which picture shows the curve C? Recall the curve C is defined by : x= f(t) cos t g(t) = sint - t y 20 20 10 10F 0 -10 -10 -20 -20 -20 10 -20 10 C 20 -10 0 10 (i) (ii) X 20 20 10 10 0 0 10 -10 -20 -20h -20 10 -20...
2. If C is the space curve given by F(t) = (t, t”, t') (0 St < 1) and F(x, y, z) = (1+z, cos(TX), e24), find ScF. dr.
4:L1-2 Consider the vector field F on Rgiven by () F(x, y) 0 and the curve c: (0,1) + R2 with 2++ + cos(t) Compute the line integral de) = ( Cand cele). \<F1ds>. { <F | do>- <insert a positive integer> Ono For partial credit, fill in the following. You can use sage-syntax, or simply write text. Note that not all ways of solving this problem depend on all fields below. Is the vector field conservative? Oyes If the...
Question 27 (Mandatory) (5 points) Production Possibilities Schedule Country X Country Y Choice Coffee Sugar Coffee Sugar А 200 0 100 o B 160 40 80 30 с 120 80 60 60 D 80 120 40 90 E 40 160 20 120 F 0 200 0 150 Reference: Ref 2-9 In the table above, if trade were to occur, which of the following is true? OA) Country X should export coffee to country Y, but the two countries should not...
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1. Consider the function f(x) e a) Find the length of the curve given by the equation y - f(x), -1 3x<1. b) Let R be the region bounded by the graph of f(x) and the lines 1,1 and y-0. Find the area of R. c) Find the coordinates of the center of mass of R. d) Consider the solid obtained by rotation of R about the r-axis. Find its volume and surface area.
1. Consider the...